Energy efficient routing with delay guarantee for sensor networks

1. Energy efficient routing with delay guarantee for sensor networks S.C., Ergen, P. Varaiya Mohammad Tariqul Islam ( Tarik )

2. Energy Efficient Routing in Sensor Networks • In WSN, sensor nodes sends collected data to the sink node. • Each of the nodes has at least one sensor, a processor, a radio, and a battery. • Batteries are non-rechargeable, hence network lifetime depends on energy efficient communication. • Related work: • Minimizing variance of residual energy at nodes • Maximize time to network partition • Minimizing cost per packet • Minimizing maximum node cost

3. Roadmap • Assumptions • Routing Algorithms (1-4) • Centralized Energy Efficient Routing • Distributed Energy Efficient Routing • Level Restricted Energy Efficient Routing • Hop Restricted Energy Efficient Routing • Space-Time Complexity • Simulation Results

4. Assumptions • The discussed WSN has one Access Point (AP) and multiple data sensor nodes. Data sensor nodes intend to send data to the AP. • Transmission power of all the sensor nodes are the same. • Each node is supported by an omnidirectional antenna, which implies that links are bidirectional: • Bidirectional links are needed for distributed Bellman-Ford algorithms. • The topology information of the sensor network is represented by a graph G = (V,E). An edge is present in the graph if both ends of it can transmit to each other

5. Assumptions (contd.) • The nodes in the network are assumed to generate data at a specific rate, which may be different for each node. • Data generated at a node is independent of the transmission structure. • The power consuming parts in a sensor node are radio, sensor and microprocessor. We assume that MAC protocol operate the radios in sleep mode when the sensor nodes are not transmitting or receiving a packet. • The operational lifetime of the sensor network is defined to be the time until the first node dies

6. Routing Algorithm -1 : Centralized Energy Efficient Routing (Contd.) • Approach: • 1) Formulate the proposed energy efficient routing method using an LP problem • 2) Prove that a directed acyclic graph satisfies the constraints in the LP • 3) Propose a method for computing a directed acyclic graph from the optimal flow rates and optimal network lifetime, and construct a directed-in-tree. • 4) Define a routing algorithm

7. Routing Algorithm -1 : Centralized Energy Efficient Routing (Contd.) The Linear Programming problem

8. Routing Algorithm -1 : Centralized Energy Efficient Routing (Contd.) A directed acyclic graph is the way to go! • Theorem 1: Consider the set of directed graphs consisting of arcs from node i to node j if and only if value of fij optimal for LP problem in Figure 1 is positive. The set includes a directed acyclic graph. • Lemma 1 An undirected graph G = (V, T) is a tree if it has |V| - 1 edges and is acyclic. • Lemma 2 Let Gv= (V, Ev) be a directed acyclic graph such that outdeg(i) = 1 for i∈ { 2, 3, …, |V|} and outdeg(1) = 0. Then Gv is a directed-in-tree rooted at node 1.

9. Routing Algorithm -1 : Centralized Energy Efficient Routing (Contd.) Construct a directed acyclic graph

10. Routing Algorithm -1 : Centralized Energy Efficient Routing (Contd.) Routing Algorithm 1: • AP floods the network with SPT-construction packet. • Each node obtains its neighbor information through the flooding • Each node sends the neighbor information to AP through the learned SPT tree. • AP solves the LP problem, and sends the optimal flow rates (fij) and optimal lifetime t0 to all the nodes. • A node uses one of the outgoing links each at each time as long as the total flow in that link is less than fijt0

11. Routing Algorithm -2: Distributed Energy Efficient Routing • Solving the LP problem requires • network topology and • packet generation rates for each node • Reasonable computation power • Approximation of LP through distributed minimum cost path problems • Goal: approximation through periodic computation of distributed routing algorithm based on residual and initial energy

12. Routing Algorithm -2: Distributed Energy Efficient Routing (contd.) • Minimize ( costpath = sum(max) of cost of the links ) • Idea: • (i) Convert undirected graph G= (V,E) to directed graph Gd = (V, Ed) • include <i,j> and <j,i> in Ed (i,j) ∈ E • (ii) Assign Cost to each link • Ci= • cost(<i,j>) = f(Ci) • (iii) Find least cost path tree from AP to all nodes for routing • Modified Bellman-Ford algorithm, hop selected depending on sum or max

13. Routing Algorithm -2: Distributed Energy Efficient Routing (contd.) Routing Algorithm: • For each Time Frame Division: • Each node computes Ci, initializes cost(i) = Inf • AP floods network with tree construction packet • Contains node cost of the upstream(sender) node, and node cost • Receiving node finds whether the sender is next hop with less cost than earlier learned paths: if (ct(j) > ct(i) + Cij) or if( ct(j) > max(ct(i) ,Cij) ) • Update node cost: ct(j) = ct(i) + Cij or ct(j) = max(ct(i) ,Cij) • Rebroadcast the packet • At the end of the flooding, a node uses best hop parent to route data

14. Delay guarantee reasoning • Energy efficient paths may be longer than shortest hop paths • Delay formulation: • Worst case delay can be higher than average case, thus violate above condition • Assumption: MAC protocol is TDMA rather than random access – needed for upper bound

15. Routing Algorithm -3 : Level Restricted Energy Efficient Routing • Bellman-Ford algorithm is used with iteration cap (i) to find shortest path with length (i) • i is computed from delay requirement • Worst case delay in the network: • upper bound: d*g*tt • Distributed Bellman-Ford is then used to find the minimum cost path of length at most dmax at each node.

16. Routing Algorithm -3 : Level Restricted Energy Efficient Routing (contd.) Routing Algorithm (similar to algorithm 2): • For each Time Division frame • AP floods network with tree construction packet. It contains • a counter (incremented at each transmission with initially being 0) c, and • nodes it has visited • The receiving node checks if the upstream(sender) node is on next hop of better path: if ( c < dmax). • Updates the packet ( if the above condition holds) by including its ID in the contained routing path, and unconditionally increases the counter by one. • Rebroadcasts the packet • At the end of the flooding, each node chooses the minimum cost path.

17. Routing Algorithm -4 : Hop Restricted Energy Efficient Routing • The Integer Programming model

18. Routing Algorithm -4 : Hop Restricted Energy Efficient Routing (Contd.) • Routing Algorithm(similar to the previous algorithm): • For Each Time Division Frame • AP floods the network with a tree construction packet. It contains • A counter, routing path, node cost, and sender node cost • Each node keeps track of paths with cost at most l: • Each receiving node finds the paths that need to updated (cost is less) and performs the action. • Rebroadcast the packet • At the end of flooding: • Each nodes knows the optimal path for each cost, sends these costs to AP. • AP finds the optimal path for each node using the Integer Programming model, sends them back to each node. • The nodes uses this path for sending data

19. Complexity of the methods • Centralized Algorithm: • Memory O(dmax) , CPU O(dmax*|V|) • Distributed Algorithm: • Memory O(1) , CPU O(dmax*|V|) • Level Restricted Routing Algorithm: • Memory O(|V|) , CPU O(dmax*|V|2) • Hop Restricted routing Algorithm: • Memory O(|V|2) , CPU O(dmax*|V|2)

20. Simulation Results Berkley mica nodes are used • Network lifetime increases by 50-150 days

21. Simulation Results (Contd.) Iterative Algorithm: • Step interval decreases => network lifetime increase ( increased iteration count) • For small step size, almost equal to least max cost path algorithms. • n should be large enough not to make d linear

22. Simulation Results (Contd.) • LR-ENR, sum, and max • Maximum number of levels beyond required for connectivity does not affect lifetime. • Implies that more allowed delay does not necessarily mean more lifetime

23. Simulation Results (Contd.) Lifetime for LR-ENR and HR-ENR • As maximum delay increases, lifetime reaches optimal value. • Uniform distribution of nodes achieves connectivity and optimal lifetime simultaneously.

24. End of Network Lifetime